Describe the Transformation
f(x) = x2 + 8
What is translation up 8.
The quadratic function translated down 3
g(x) = x2 - 3
f(x) = x2
Even
1) Identify the vertex of the below equation.
2) Will the function be opening up or down?
f(x)= (x+3)2-7
Vertex: (-3, -7)
Function will be opening up.
Suppose we have the function f(x)=(x+3)2-7, and this function is being translated down by 2 units. What will the new function, g(x) be?
g(x)=(x+3)2-9
The absolute value function translated to the left 7 and stretched vertically by a factor of 1/5.
f(x) = 1/5lx + 7l
h(x) = -x3-4x+5
Neither
1) Identify the vertex of the below equation.
2) Will the function be opening up or down?
f(x)= x2-2x+1
Vertex: (-1, 0)
Function will open up
Suppose we have the function f(x)=(x+3)2-7, and this function is being translated up by 10 units and translated to the right by 6 units. What will the new function, g(x) be?
g(x)=(x-3)2+3
f(x) = 1/2x3 - 5
What is Compression by 1/2 and down 5.
Let f(x)=(x-3)3-7. g(x) is the f(x) after it is shifted to the right by 5. What will g(x) be?
g(x)= (x-8)2-7
Suppose the point (-6, -10) is a point on an even function. What has to be another point on this function?
(6, -10)
1) Identify the vertex of the below equation.
2) Will the function be opening up or down?
f(x)= x2-10x-26
(5, -51)
Function will open up
Suppose we have the function f(x)=sqrt(x-6)+9, and this function is being translated down by 10 units, translated to the left by 10 units, and reflected across the x-axis. What will the new function, g(x) be?
g(x)=-sqrt(x+4)-1
f(x) = -(x + 9) - 2
What is reflection across x-axis, translates left 9 and down 2.
Let f(x)=-|x+5|+5. g(x) is the f(x) after it is reflected across the x-axis, shifted to the right by 8, and shifted down by 7. What will g(x) be?
g(x)=|x-3|-2
Suppose the point (-6, -10) is a point on an odd function. What has to be another point on this function?
(6, 10)
1) Identify the vertex of the below equation.
2) Will the function be opening up or down?
f(x)= -x2-6x+8
(-3, -17)
Function will open down
Suppose I have the function f(x)=(x-6)3+2, and its transformed function is g(x)=-1/3(x-5)2-4. What transformations have been applied to f(x) to get g(x)?
The function has been reflected across the x-axis, vertically compressed by a factor or 1/3, shifted down by 6 units, and shifted to the left by 1 unit.
f(x) = -3lx - 5l - 6
What is reflection across x-axis, stretch by a factor of 3, translates right 5 and down 6
Let f(x)=(x+2). g(x) is the f(x) after it is reflected across the x-axis, shifted to the right by 8, and shifted down by 7. What will g(x) be?
What is g(x) = -2lx + 3l + 4
g(x) =(x - 5)2
Neither
1) Identify the vertex of the below equation.
2) Will the function be opening up or down?
f(x)= -6x2-12x+1
(-1, 7)
Opens Down
Suppose I have the function f(x)=(x-6)3+2, and its transformed function is g(x)=-1/3(x-5)2-4. What transformations can be applied to g(x) in order to get f(x)?
We can reflect g(x) across the x-axis, vertically stretch it by a factor of 3, shift it to the right by 1, and shift it up by 6.